Volume 6, Number 1, January 2000 Copyright © 2000 Society for Music Theory Willie Anku KEYWORDS: African music, rhythm, dance music, set theory ABSTRACT: Much of African music is circular. This circular concept of time ultimately defines a structural set. The set represents a structural module from which the entire performance is derived. The performance consists of a steady ostinato framework of multi-concentric rhythms on which various manipulations of the set are realized by a leader (e.g., a lead drummer). It is in these complex structural manipulations (against a background of a steady ostinato referent) that Africa finds its finest rhythmic qualities. The paper focuses on two principal elements. It discusses the properties of the rhythmic set, and it demonstrates its various modes of performance and analytical applications. Introduction [1] For the sake of those who are not well acquainted with the procedures of African music, I would like to begin by presenting, in brief, a general (descriptive) analytical picture of its performance practice. I would like first of all, to distinguish between two broad categories of music practiced in Africa as those that are strictly timed (or metered), often suited for dance and those that lack in dance qualities and therefore, for the want of an appropriate term, may be described as in “free rhythm.” This paper focuses on the former, which finds its highest expression in “dance drumming.” Though African community life makes provision for individual music making, music is generally organized as a social event, oriented towards a large degree of community participation. Following are four structural statements about the music: [2] 1. Whether performed individually or shared as a collective experience, the music is nonetheless rigidly controlled by a recurrent rhythm often associated with the role of the bell pattern typical of West and Central African drumming. This controlling structural concept is however not always externalized along with the music. It prevails mentally and controls its structural perception, as for instance in the case of a lone performer playing a xylophone or Mbira/Kalimba—“thumb piano.” [3] 2. This time Line concept of the bell rhythm (for the purpose of this paper) translates as a time cycle because African music is perceived essentially as a circular concept rather than linear (Figure 1). Events of the performance (which may include multiple instruments, a body of songs and dances) are all organized around this structural matrix, making it possible for performers to go in and out of the performance without much inhibition. There are however clearly prescribed cues for each event. [4] 3. The events are unified by a common recurring undercurrent of one regulative beat per cycle which is divided into four equidistant beats. The regulative beat with its equidistant beat divisions should not be misconstrued for a metric concept. Instead, it is a structural definition of the time cycle span. All the composite parts of the performance are controlled, 1 of 8 however, by a single meter. [5] 4. The drum ensemble consists of two basic concepts—the background ostinato on one hand and the master drum concept on the other. Visualize the background ostinato as consisting of concentric circular rhythms, each with its peculiar orientation to the regulative beat of the time cycle and thus revealing staggered entry relationships astride the regulative beat. Against this constant ostinato structural framework of the background, the master drum “projects” a succession of intriguing, logically ordered rhythmic manipulations which are concurrently regulated by the common timing principle of the time cycle. A visual representation reveals a complex interlocking super-structure of the fundamental circular concept (Figure 2). The Quantification Process (The Transcription) [6] Ideally, African music is highly quantifiable. To the uncultivated listener, such a statement may seem an absolute absurdity at first. While the music seems to emerge from a principle of collective social participation with a high incidence of social interaction, nevertheless, its practitioners have a developed sense of tolerance for certain apparent disparities that may be manifest during performance. Thus, knowledge of the “compositional ideal” exists in each ethnic tradition and is available from those regarded as musicians in society on the critical level, and the community at large on the general level. A reliable transcription ought to take full cognizance of precise rhythmic relationships and “ethnic perception norms” on the appropriate level of inquiry and should not be dependent merely on performance manifestations. [7] African music is isometric. The music is either or . is rarely or never used in African music. The Analytical Framework [8] The time cycle ultimately defines a set and this set rhythm is a structural module from which the entire performance is derived. Having said that, my first task is to isolate the constituent set properties as follows. It consists of (Figure 3) . : four equidistant beat areas, one occurrence of a regulative beat (marked with a down arrow in the following figures), polarization into two symmetrical halves. [9] There are three identifiable set types: The 12-time point set: (with an eighth-note referent)—spans two measures of time (Figure 4). The 16-time point set: (with a sixteenth-note referent)—spans two measures of time (Figure 5). The cross-set (combines elements of the 12 and 16 sets is of two kinds— a. A cross-set with a 12 primary set is a meter with tuplets, b. A cross-set with a 16 primary set is simply a meter consisting of triplets. [10] Drum pieces belong to one set or the other at any given time. Coincidentally, these sets are observed to convey particular moods which make each one contextually appropriate. For instance, pieces in the 12 set category are found to be associated with occasions of serious social and festive nature, such as funerals and celebrations involving royalty. A large number of pieces in the 16 set are for recreational purposes and are of light, less serious (social) content. Those of the cross-set (particularly the 16 phenomenon) are associated with ritual, worship, prowess, and related contexts. The Syntax of Set Rhythm [11] To understand rhythm syntax we need to consider that it consists of both physical and psychological properties, that is, the rhythm itself on a superficial level and the way it is perceived, on a deeper level. When we hear rhythm without any preconceived beat indications, there is a natural tendency to assume a self-determined perception based on our memory of a previous experience. Hearing therefore is subjectively conditioned by our choice of perception. This, of course, does not necessarily represent the way the rhythm is transmitted, resulting in an obvious disparity between the perception of the transmitter and that of the recipient. [12] In Western art music, this problem of disparity is forestalled by the externalization of meter with the use of time signatures. In African music the counterpart of the metric solution prevails, though intuitively, in ethnically perceived norms of beat perception. So therefore, if the rhythm in Figure 6 is played in reference to a particular genre of an ethnic tradition, 2 of 8 it is likely to be misconstrued by one unfamiliar with its beat perception norms of that tradition, as for example in Figure 7. The two rhythms are practically the same on the superficial level, that is, without externalization of their beat perceptions (see Figure 8). There are sixteen different beat perception possibilities in this concept, considering that each time-point of the set (based on a sixteenth note referent), is a potential first beat in rotation within the cycle. [13] In view of the above, I have suggested a paradigm of five attributes to help define and describe set rhythms as follows. 1. Indicate the rhythm first by its set type (whether 12,16, or cross-set). The rhythm in Figure 9 is a 12 set. 2. Next, indicate the number of attack points in the set. Our example shows 7 of those. 3. Drum traditions perceive each set rhythm with a definite beginning and ending. Our example has a time interval order of 2212221. [14] To describe a specific set rhythm considering its embedded rotational possibilities, we will need to establish an arbitrary standard as the prime form (normal form). By definition the prime form is the set rotation with the least time interval arrangement at the beginning in “unordered” form—thus, from the fastest to the slowest arrangement of the rotation. In this case the prime form of [2212221] is [1221222]. 4. With the prime form digits numbered 0 to 6, the original pattern—2212221 will be described as rotation 1 (R1) of the prime form. 1 2 2 1 2 2 2 | | | | | | | 0 1 2 3 4 5 6 5. The fifth and last element for consideration is the regulative beat. Since the composite set rhythms of the ensemble establish definite orientations with the regulative beat, it is a good indicator to establish set relationships. And since the regulative beat occurs on one of the time points of each set rhythm, it is expedient to label it Regulative Time Point (RTP) instead of regulative beat. The RTP position describes the regulative beat position (indicated by an arrow) of the original pattern and not of the prime form. The RTP of our example is therefore, RTP1 (see Figure 10). [15] This rhythm and its perception is peculiar to Anlo Ewe of Ghana and used in musical types such as agbadza, adzogbo, etc. The schematic analyses in Figures 11a through 11d demonstrate that the same Ewe rhythm [2212221] would be perceived differently by the Yoruba of Nigeria and the Bemba of Central Africa. [16] Observe that all three rhythms share the same set type, number of attack points and prime form on the superficial level, but different perception of their rotations within the prime form and RTP orientations, on a deeper ethnic level.